Select the correct S.I. unit for surface tension (force per unit length at a liquid interface).

Difficulty: Easy

kg/m^3
kg/m^2
kg/m
N/m
Pa·s

Correct Answer: N/m

Explanation:

Introduction / Context:
Surface tension quantifies the tangential force acting along a line at a liquid interface. It strongly affects capillarity, droplet formation, bubble stability, and wetting phenomena. Using the correct S.I. unit ensures formulas like rise in a capillary or pressure jump across a curved interface are applied consistently.

Given Data / Assumptions:

Surface tension is force per unit length.
Force in S.I. is newton (N).
Length in S.I. is metre (m).

Concept / Approach:
By definition, T = F / L. Therefore the unit must be N/m in S.I. This distinguishes surface tension from stress (N/m^2), density (kg/m^3), and dynamic viscosity (Pa·s). Remember this when decoding mixed-unit problem statements, especially those involving capillary tubes and contact angles.

Step-by-Step Solution:

State definition: T = F / L.Insert S.I. units: F → N; L → m; thus T → N/m.Confirm with typical values: water at room temperature ≈ 0.072 N/m.

Verification / Alternative check:

Check capillary-rise formula where surface tension multiplies a length and cosine term, yielding force units, consistent with T in N/m.

Why Other Options Are Wrong:

kg/m^3: density.kg/m^2 or kg/m: do not reduce to force/length.Pa·s: dynamic viscosity, not surface tension.

Common Pitfalls:

Confusing surface tension with pressure (N/m^2) due to both involving forces.Expecting a mass-based unit because many fluid properties use kg and m^3; surface tension is fundamentally force/length.

Final Answer:

N/m

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Select the correct S.I. unit for surface tension (force per unit length at a liquid interface).

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